diff --git a/README.md b/README.md --- a/README.md +++ b/README.md @@ -1,7 +1,7 @@ group-theory ========== -[![Hackage](https://img.shields.io/hackage/v/group-theory.svg)](https://hackage.haskell.org/package/group-theory) ![Build Status](https://github.com/emilypi/group-theory/workflows/ci/badge.svg) +[![Hackage](https://img.shields.io/hackage/v/group-theory.svg)](https://hackage.haskell.org/package/group-theory) ![Build Status](https://github.com/emilypi/group-theory/workflows/Haskell-CI/badge.svg) This is a package for exploring constructive group theory in Haskell. diff --git a/group-theory.cabal b/group-theory.cabal --- a/group-theory.cabal +++ b/group-theory.cabal @@ -1,7 +1,7 @@ -cabal-version: 2.0 -name: group-theory -version: 0.2.0.0 -synopsis: The theory of groups +cabal-version: 2.0 +name: group-theory +version: 0.2.1.0 +synopsis: The theory of groups description: This package includes definitions for Groups (Monoids with invertibility), including order calculations as well as finite, free, cyclic, and permutation groups. Additionally, we add the concept @@ -17,31 +17,28 @@ . This package, @group-theory@, tries to combine the best parts, while focusing on usability and intuitiveness. -homepage: https://github.com/emilypi/group-theory -bug-reports: https://github.com/emilypi/group-theory/issues -license: BSD3 -license-file: LICENSE -author: Emily Pillmore -maintainer: Emily Pillmore , Reed Mullanix -copyright: (c) 2020 Emily Pillmore -category: Algebra, Math, Permutations, Groups -build-type: Custom -extra-doc-files: +homepage: https://github.com/emilypi/group-theory +bug-reports: https://github.com/emilypi/group-theory/issues +license: BSD3 +license-file: LICENSE +author: Emily Pillmore +maintainer: + Emily Pillmore , Reed Mullanix + +copyright: (c) 2020-2021 Emily Pillmore +category: Algebra, Math, Permutations, Groups +build-type: Simple +extra-source-files: CHANGELOG.md README.md -tested-with: GHC ==8.4.4 || ==8.6.5 || ==8.8.4 || ==8.10.2 +tested-with: + GHC ==8.4.4 || ==8.6.5 || ==8.8.4 || ==8.10.4 || ==9.0.1 source-repository head type: git location: https://github.com/emilypi/group-theory.git -custom-setup - setup-depends: - base >=4.11 && <5 - , Cabal - , cabal-doctest - library exposed-modules: Control.Applicative.Cancellative @@ -51,31 +48,18 @@ Data.Group.Finite Data.Group.Foldable Data.Group.Free - Data.Group.Free.Internal Data.Group.Free.Church + Data.Group.Free.Internal Data.Group.Free.Product Data.Group.Multiplicative Data.Group.Order Data.Group.Permutation build-depends: - base >=4.11 && <5 - , containers >=0.5 && <0.7 + base >=4.11 && <5 + , containers >=0.5 && <0.7 , groups ^>=0.5.2 hs-source-dirs: src default-language: Haskell2010 ghc-options: -Wall - -test-suite doctests - default-language: Haskell2010 - type: exitcode-stdio-1.0 - main-is: doctests.hs - build-depends: - base >=4.11 && <5 - , doctest - , group-theory - - hs-source-dirs: test - ghc-options: -Wall -threaded - x-doctest-options: --fast diff --git a/src/Control/Applicative/Cancellative.hs b/src/Control/Applicative/Cancellative.hs --- a/src/Control/Applicative/Cancellative.hs +++ b/src/Control/Applicative/Cancellative.hs @@ -31,8 +31,9 @@ -- $setup -- --- >>> import qualified Prelude --- >>> import Data.Group +-- >>> :set -XPackageImports +-- >>> import Prelude +-- >>> import "group-theory" Data.Group -- >>> import Data.Monoid -- >>> import Data.Semigroup -- >>> import Data.Word diff --git a/src/Data/Group.hs b/src/Data/Group.hs --- a/src/Data/Group.hs +++ b/src/Data/Group.hs @@ -10,7 +10,7 @@ {-# language ViewPatterns #-} -- | -- Module : Data.Group --- Copyright : (c) 2020 Emily Pillmore +-- Copyright : (c) 2020-2021 Emily Pillmore -- License : BSD-style -- -- Maintainer : Emily Pillmore , @@ -56,8 +56,9 @@ -- $setup -- +-- >>> :set -XPackageImports -- >>> import qualified Prelude --- >>> import Data.Group +-- >>> import "group-theory" Data.Group -- >>> import Data.Monoid -- >>> import Data.Semigroup -- >>> import Data.Word @@ -230,11 +231,11 @@ Commuted a <> Commuted b = Commuted (a <> b) instance Monoid g => Monoid (Abelianizer g) where - -- Normally we'd say 'Quot' but these are the same. - mempty = Commuted mempty + mempty = Quot instance (Eq g, Group g) => Group (Abelianizer g) where invert Quot = Quot + invert (Commuted IdentityElem) = Quot invert (Commuted a) = Commuted (invert a) -- | Take the commutator of two elements of a group. diff --git a/src/Data/Group/Additive.hs b/src/Data/Group/Additive.hs --- a/src/Data/Group/Additive.hs +++ b/src/Data/Group/Additive.hs @@ -3,7 +3,7 @@ {-# language Safe #-} -- | -- Module : Data.Group.Additive --- Copyright : (c) 2020 Emily Pillmore +-- Copyright : (c) 2020-2021 Emily Pillmore -- License : BSD-style -- -- Maintainer : Emily Pillmore , @@ -43,9 +43,10 @@ infixl 7 × -- $setup --- +-- >>> :set -XPackageImports +-- >>> import Prelude (Int) -- >>> import qualified Prelude --- >>> import Data.Group +-- >>> import "group-theory" Data.Group -- >>> import Data.Monoid -- >>> import Data.Semigroup -- >>> :set -XTypeApplications diff --git a/src/Data/Group/Cyclic.hs b/src/Data/Group/Cyclic.hs --- a/src/Data/Group/Cyclic.hs +++ b/src/Data/Group/Cyclic.hs @@ -3,7 +3,7 @@ {-# language Safe #-} -- | -- Module : Data.Group.Cyclic --- Copyright : (c) 2020 Emily Pillmore +-- Copyright : (c) 2020-2021 Emily Pillmore -- License : BSD-style -- -- Maintainer : Emily Pillmore , @@ -26,9 +26,9 @@ import "groups" Data.Group as G -- $setup --- --- >>> import qualified Prelude --- >>> import Data.Group +-- >>> :set -XPackageImports +-- >>> import Prelude +-- >>> import "group-theory" Data.Group -- >>> import Data.Monoid -- >>> import Data.Semigroup -- >>> import Data.Word diff --git a/src/Data/Group/Finite.hs b/src/Data/Group/Finite.hs --- a/src/Data/Group/Finite.hs +++ b/src/Data/Group/Finite.hs @@ -4,7 +4,7 @@ {-# language Safe #-} -- | -- Module : Data.Group.Finite --- Copyright : (c) 2020 Emily Pillmore +-- Copyright : (c) 2020-2021 Emily Pillmore -- License : BSD-style -- -- Maintainer : Emily Pillmore , @@ -35,9 +35,9 @@ import Numeric.Natural (Natural) -- $setup --- --- >>> import qualified Prelude --- >>> import Data.Group +-- >>> :set -XPackageImports +-- >>> import Prelude +-- >>> import "group-theory" Data.Group -- >>> import Data.Monoid -- >>> import Data.Semigroup -- >>> import Data.Word diff --git a/src/Data/Group/Foldable.hs b/src/Data/Group/Foldable.hs --- a/src/Data/Group/Foldable.hs +++ b/src/Data/Group/Foldable.hs @@ -6,7 +6,7 @@ #endif -- | -- Module : Data.Group --- Copyright : (c) 2020 Reed Mullanix, Emily Pillmore +-- Copyright : (c) 2020-2021 Reed Mullanix, Emily Pillmore -- License : BSD-style -- -- Maintainer : Reed Mullanix , @@ -43,9 +43,10 @@ -- $setup --- --- >>> import qualified Prelude --- >>> import Data.Group +-- >>> :set -XPackageImports +-- >>> import Prelude +-- >>> import "group-theory" Data.Group +-- >>> import Data.Group.Free -- >>> import Data.Monoid -- >>> import Data.Semigroup -- >>> import Data.Word diff --git a/src/Data/Group/Free.hs b/src/Data/Group/Free.hs --- a/src/Data/Group/Free.hs +++ b/src/Data/Group/Free.hs @@ -2,7 +2,7 @@ {-# language Trustworthy #-} -- | -- Module : Data.Group.Free --- Copyright : (c) 2020 Reed Mullanix, Emily Pillmore +-- Copyright : (c) 2020-2021 Reed Mullanix, Emily Pillmore -- License : BSD-style -- -- Maintainer : Reed Mullanix , @@ -46,12 +46,13 @@ import Data.Group import Data.Group.Free.Internal import Data.Group.Order -import Data.Semigroup(Semigroup(..)) + -- $setup -- --- >>> import qualified Prelude --- >>> import Data.Group +-- >>> :set -XPackageImports +-- >>> import Prelude +-- >>> import "group-theory" Data.Group -- >>> import Data.Monoid -- >>> import Data.Semigroup -- >>> import Data.Word diff --git a/src/Data/Group/Free/Church.hs b/src/Data/Group/Free/Church.hs --- a/src/Data/Group/Free/Church.hs +++ b/src/Data/Group/Free/Church.hs @@ -2,7 +2,7 @@ {-# language Safe #-} -- | -- Module : Data.Group --- Copyright : (c) 2020 Reed Mullanix, Emily Pillmore +-- Copyright : (c) 2020-2021 Reed Mullanix, Emily Pillmore -- License : BSD-style -- -- Maintainer : Reed Mullanix , diff --git a/src/Data/Group/Free/Internal.hs b/src/Data/Group/Free/Internal.hs --- a/src/Data/Group/Free/Internal.hs +++ b/src/Data/Group/Free/Internal.hs @@ -1,7 +1,7 @@ {-# language Unsafe #-} -- | -- Module : Data.Group.Free.Internal --- Copyright : (c) 2020 Reed Mullanix, Emily Pillmore, Koji Miyazato +-- Copyright : (c) 2020-2021 Reed Mullanix, Emily Pillmore, Koji Miyazato -- License : BSD-style -- -- Maintainer : Reed Mullanix , @@ -28,12 +28,13 @@ -- $setup --- --- >>> import qualified Prelude --- >>> import Data.Group +-- >>> :set -XPackageImports +-- >>> import Prelude +-- >>> import "group-theory" Data.Group -- >>> import Data.Monoid -- >>> import Data.Semigroup -- >>> import Data.Word +-- >>> import qualified Data.Map as Map -- >>> :set -XTypeApplications -- >>> :set -XFlexibleContexts diff --git a/src/Data/Group/Free/Product.hs b/src/Data/Group/Free/Product.hs --- a/src/Data/Group/Free/Product.hs +++ b/src/Data/Group/Free/Product.hs @@ -1,6 +1,6 @@ -- | -- Module : Data.Group.Free.Product --- Copyright : (c) 2020 Reed Mullanix, Emily Pillmore +-- Copyright : (c) 2020-2021 Reed Mullanix, Emily Pillmore -- License : BSD-style -- -- Maintainer : Reed Mullanix , diff --git a/src/Data/Group/Multiplicative.hs b/src/Data/Group/Multiplicative.hs --- a/src/Data/Group/Multiplicative.hs +++ b/src/Data/Group/Multiplicative.hs @@ -2,7 +2,7 @@ {-# language Safe #-} -- | -- Module : Data.Group.Multiplicative --- Copyright : (c) 2020 Emily Pillmore +-- Copyright : (c) 2020-2021 Emily Pillmore -- License : BSD-style -- -- Maintainer : Emily Pillmore , @@ -39,8 +39,10 @@ -- $setup -- --- >>> import qualified Prelude --- >>> import Data.Group +-- >>> :set -XPackageImports +-- >>> import Prelude (Int, Rational) +-- >>> import qualified Prelude as P +-- >>> import "group-theory" Data.Group -- >>> import Data.Monoid -- >>> import Data.Semigroup -- >>> :set -XTypeApplications diff --git a/src/Data/Group/Order.hs b/src/Data/Group/Order.hs --- a/src/Data/Group/Order.hs +++ b/src/Data/Group/Order.hs @@ -4,7 +4,7 @@ {-# language ViewPatterns #-} -- | -- Module : Data.Group.Order --- Copyright : (c) 2020 Emily Pillmore +-- Copyright : (c) 2020-2021 Emily Pillmore, -- Koji Miyazato -- License : BSD-style -- @@ -42,6 +42,15 @@ import Numeric.Natural (Natural) +-- $setup +-- +-- >>> :set -XPackageImports +-- >>> import "group-theory" Data.Group +-- >>> import Data.Monoid +-- >>> import Data.Semigroup +-- >>> import Data.Word +-- >>> :set -XTypeApplications +-- >>> :set -XFlexibleContexts -- -------------------------------------------------------------------- -- -- Group order diff --git a/src/Data/Group/Permutation.hs b/src/Data/Group/Permutation.hs --- a/src/Data/Group/Permutation.hs +++ b/src/Data/Group/Permutation.hs @@ -6,7 +6,7 @@ {-# language ViewPatterns #-} -- | -- Module : Data.Group --- Copyright : (c) 2020 Emily Pillmore +-- Copyright : (c) 2020-2021 Emily Pillmore -- License : BSD-style -- -- Maintainer : Reed Mullanix , @@ -22,6 +22,9 @@ ( -- * Permutation groups Permutation(..) -- ** Permutation group combinators +, equalPermutation +, comparePermutation +, orderOfPermutation , permute , pairwise , (-$) @@ -34,7 +37,6 @@ import Data.Group -import Data.Group.Order import qualified Data.IntSet as ISet import Data.Function (on) @@ -67,10 +69,10 @@ -- and computed their 'order's. -- -- >>> c1 = permute not not :: Permutation Bool --- >>> c1 <> c1 == mempty +-- >>> equalPermutation (c1 <> c1) mempty -- True --- >>> order c1 --- Finite 2 +-- >>> orderOfPermutation c1 +-- 2 data Permutation a = Permutation { to :: a -> a -- ^ The forward half of the bijection @@ -90,14 +92,59 @@ instance Group (Permutation a) where invert (Permutation t f) = Permutation f t -instance (Enum a, Bounded a) => Eq (Permutation a) where - (==) = (==) `on` (functionRepr . to) +-- | Equality test for permutations on a finite type 'a' +-- +-- This module /intentionally omits/ the following instance, albeit +-- 'equalPermutation' is suitable implementation of +-- @(==)@ operator for many types. +-- +-- > instance (Enum a, Bounded a) => Eq (Permutation a) where +-- > (==) = equalPermutation +-- +-- This is because some type satisfying @(Enum a, Bounded a)@ are +-- actually finite but too large to use @equalPermutation@ on. +-- For example, you can call @equalPermutation@ on @Permutation Int@, +-- but it takes too much computation to be considered usable. +equalPermutation + :: (Enum a, Bounded a) => Permutation a -> Permutation a -> Bool +equalPermutation = (==) `on` (functionRepr . to) -instance (Enum a, Bounded a) => Ord (Permutation a) where - compare = compare `on` (functionRepr . to) +-- | Comparison for permutations on a finite type 'a' +-- +-- This module /intentionally omits/ the following instance, albeit +-- 'comparePermutation' is suitable implementation of +-- @compare@ method for many types. +-- +-- > instance (Enum a, Bounded a) => Eq (Permutation a) where +-- > compare = comparePermutation +-- +-- This is because some type satisfying @(Enum a, Bounded a)@ are +-- actually finite but too large to use @comparePermutation@ on. +-- For example, you can call @comparePermutation@ on @Permutation Int@, +-- but it takes too much computation to be considered usable. +comparePermutation + :: (Enum a, Bounded a) => Permutation a -> Permutation a -> Ordering +comparePermutation = compare `on` (functionRepr . to) -instance (Enum a, Bounded a) => GroupOrder (Permutation a) where - order Permutation{to = f} = Finite (go 1 fullSet) +functionRepr :: (Enum a, Bounded a) => (a -> a) -> [Int] +functionRepr f = fromEnum . f <$> [minBound .. maxBound] + +-- | Order counting for a permutation on a finite type 'a' +-- +-- This module /intentionally omits/ the following instance, albeit +-- 'orderOfPermutation' is suitable implementation of +-- @order@ method for many types. +-- +-- > instance (Enum a, Bounded a) => GroupOrder (Permutation a) where +-- > order a = Finite (orderOfPermutation a) +-- +-- This is because some type satisfying @(Enum a, Bounded a)@ are +-- actually finite but too large to use @orderOfPermutation@ on. +-- For example, you can call @orderOfPermutation@ on @Permutation Int@, +-- but it takes too much computation to be considered usable. +orderOfPermutation + :: forall a. (Enum a, Bounded a) => Permutation a -> Natural +orderOfPermutation Permutation{to = f} = go 1 fullSet where n = 1 + fromEnum (maxBound @a) fullSet = ISet.fromDistinctAscList [0 .. n - 1] @@ -107,7 +154,7 @@ go :: Natural -> ISet.IntSet -> Natural go !ord elements = case ISet.minView elements of - Nothing -> ord + Nothing -> ord Just (k, elements') -> let (period, elements'') = takeCycle k elements' in go (lcm period ord) elements'' @@ -116,14 +163,9 @@ takeCycle k = loop 1 (f' k) where loop !period j elements - | j `ISet.member` elements = loop (succ period) (f' j) (ISet.delete j elements) + | j `ISet.member` elements = loop (succ period) (f' j) (ISet.delete j elements) | {- j ∉ elements && -} j == k = (period, elements) - | otherwise = error $ "Non-bijective: witness=toEnum " ++ show j - --- | Apply a function to all enumerated elements of a bounded enumerable type --- -functionRepr :: (Enum a, Bounded a) => (a -> a) -> [Int] -functionRepr f = fromEnum . f <$> [minBound .. maxBound] + | otherwise = error $ "Non-bijective: witness=toEnum " ++ show j -- -------------------------------------------------------------------- -- -- Permutation group combinators diff --git a/test/doctests.hs b/test/doctests.hs deleted file mode 100644 --- a/test/doctests.hs +++ /dev/null @@ -1,7 +0,0 @@ -module Main where - -import Build_doctests (flags, pkgs, module_sources) -import Test.DocTest (doctest) - -main :: IO () -main = doctest $ flags ++ pkgs ++ module_sources